527 
Tbe composition of each phase is given in terms of the absolute 
quantity in mols of each component. Between these quantities the 
following relations subsist: 
: 2, + @,+.....4% =X | 
gia Pica ee bine nd 
zl a (1) 
Zi = 2s = eee: 2 == 
The number of equations in (1) is n. The quantities X, Y,S..., 
which determine the total composition, are to be considered constant. 
If we represent the ¢-functions of the separate phases by Z,,Z,,...Z), 
the equilibrium conditions are: 
aZ, 0Z, © eZ, Zn on ; OZ, OZ a 
Pe Oe DOr | RS Loe dee” 
a a7 
|) CRO 5, SE Soya Oe Oe iy. en) 
dy, oy, dy, Oy, Oy. Oy, 
The number of equations (2) is n (/—1). 
With regard to the form of these equations it may be noted that. 
the expressions on the left are homogeneous functions of degree 0 with 
respect to the variables z,, 7,,...., and are thus only dependent on the 
ratios of these variables to each other (ee, al atc.) and not 
U, U, 
on the absolute values. Besides p and 7’ we have therefore only 
/(n—1) unknowns or variables, since in each phase there are only 
n—1 ratios which determine the composition. 
If /=n, we have n (n—1) equations (2) with m(n—1) unknowns 
(besides p and 7’). For given values of p and 7’ the composition 
is thus completely determined by these equations and is thus in- 
dependent of the total composition X, Y,.... Equations (1) serve 
only for the calculation of the absolute values of w,, etc. 
If /<n, we have fewer equations (2) than unknowns which 
determine the composition of each phase. In this case for the cal- 
culation of the composition of the phases we must make use of the 
equations (1), so that the composition of each phase is dependent 
on the total composition. 
We have, however, always a sufficient number of equations for 
the calculation of the composition of each phase for a given value 
of p and 7, for we have n +n(/—1)=n/ equations in x/ unknown 
quantities #,,4,,...2,,7,,--. in which p and 7' can be considered 
as the independent variables. 
do” 
